Although primarily a populariser, Finé was one of the most prolific authors of mathematical books of his age. He worked in a wide range of mathematical fields, including practical geometry, arithmetic, optics, gnomonics, astronomy and instrumentalism.[4]

He gave the value of pi (≈ 3.14159) to be ​222⁄9/7 ≈ 3.1746 in 1544. Later, he gave 47/15 ≈ 3.1333 and, in De rebus mathematicis (1556), he gave 311/78 ≈ 3.1410.

In 1542 Finé published De mundi sphaera (On the Heavenly Spheres), a popular astronomy textbook whose woodcut illustrations were much appreciated.[5] His writing on astronomy included guides to the use of astronomical equipment and methods (e.g. the ancient practice of determining longitude through the coordinated observation of lunar eclipses from two fixed points with enough distance between them to make the phenomena appear at different times of the night). He also described more recent innovations, such as an instrument he called a méthéoroscope (an astrolabe modified by adding a compass).

Explanatory work was complemented by direct contributions. His woodcut map of France (1525) is one of the first of its kind. He constructed an ivorysundial in 1524, which still exists.[6]

Finé attempted to reconcile discoveries in the New World with old medieval legends and information (derived from Ptolemy) regarding the Orient. Thus, on one of his two world maps, Nova Universi Orbis Descriptio (1531), the legend marked Asia covers both North America and Asia, which were represented as one landmass. He used the toponym "America" for South America, and thus Marco Polo's Mangi, Tangut and Catay appear on the shores of the present-day Gulf of Mexico. On the same map, Finé drew Terra Australis to the south, including the legend "recently discovered but not yet completely explored", by which he meant the discovery of Tierra del Fuego by Ferdinand Magellan.[8]

Finé's cosmography was derived from the German mathematician and cosmographer Johannes Schöner.[9] In his study of Schöner's globes, Franz von Wieser, found that the derivation of Finé's mappemonde from them was "unmistakeable (unverkennbar)"; he said "Orontius Finaeus took from Schöner not only the 'Brasilie Regio'", but the whole Austral Continent, the Strait of Magellan, and above all the whole arrangement of lands; in a word, the mappemonde of Oronce Finé is a copy of Schöner's".[10] Lucien Gallois also noted the undeniable ressemblance parfaite between Finé's 1531 mappemonde and Schöner's globe of 1533.[11] As Schöner's globe of 1523, which also closely resembled Finé's mappemonde, was not identified until 1925 by Frederik (F.C.) Wieder, Gallois was forced to argue that Finé, who said he had been working on his mappemonde since 1521, had had direct or indirect personal communication with Schöner or had drawn upon his 1515 Luculentissima descriptio. Wieder's identification of Schöner's map gores of 1523 strengthens Gallois' case for Finé's reliance upon Schöner.[12]

Fine's 1536 world map bore a dedicatory inscription in the lower left corner, which stated:

ABOUT FIFTEEN years since, Dear Reader, we first designed, in the shape of a human heart, this universal map of the world, in gratitude to the Most Christian and Most Mighty Francis, King of the French, our most clement Maecenas. For while we saw the King, a Polymath, and uncommon Geographer, greatly pleased by all and praised by many, even in foreign countries, I wanted finally to communicate the same description of the whole globe to all students of Mathematics: which, after variations in fortune and crises in the studies we pursued, which up to now have been a hindrance to us, we have finally done at our own risk. And so, augmented and corrected by many observations of modern hydrographers, the same heart-shaped geographical image for yourself, devoted reader and for all men of goodwill, we present to a wise and liberal mind. It remains, therefore, that you will not refuse to accept this labour and industry of ours with a human appearance, and fairly and well consult it. Finally, while we strive ever more earnestly for the favour and generosity of our Most Christian and magnificent King, whose happiness and success you eagerly desire, we have shared this with you. Farewell, from Paris.[13]

^For the debate over the French spelling of Finé's name see Alexander Marr, 'Introduction', in 'The Worlds of Oronce Fine: Mathematics, Instruments and Print in Renaissance France' (Shaun Tyas, 2009), pp. 1–12. Finé's name is often found spelt with an acute accent, but the Dictionnaire de Biographie française (ed. Roman D'Amat, Paris, 1975, p.1370) gives a very definite direction that his name should be spelt without an accent, "Fine, et non Finé".